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All Textbook Solutions for Intermediate Algebra

In the following exercises, simplify each expression. 489. 80.05 In the following exercises, simplify each expression. 490. 121 In the following exercises, simplify each expression. 491. (813+57)+27 In the following exercises, simplify each expression. 492. 5x+(8y)6x+3y In the following exercises, simplify each expression. 493. (a) 09 (b) 110 In the following exercises, simplify each expression. 494. 3(8x5)In the following exercises, simplify each expression. 495. 6(3y1)(5y3)Determine whether the values are solutions to the equation: 9y+2=6y+3 . (a) y=43 (b) y=13 Determine whether the values are solutions to the equation: 4x2=2x+1 . (a) x=32 (b) x=12 Solve: 2(m4)+3=1 .Solve: 5(a3)+5=10 .Solve: 13(6u+3)=7u .Solve: 23(9x12)=8+2x .Solve: 6(p3)7=5(4p+3)12 .Solve: 8(q+1)5=3(2q4)1 .Solve: 6[42(7y1)]=8(138y) .Solve: 12[15(4z1)]=3(24+11z) .Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: 4+9(3x7)=42x13+23(3x2) .Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: 8(13x)+15(2x+7)=2(x+50)+4(x+3)+1 .Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: 11(q+3)5=19 Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: 6+14(k8)=95 Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: 12c+5(5+3c)=3(9c4)Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: 4(7d+18)=13(3d2)11d Solve: 14x+12=58 .Solve: 18x+12=14 .Solve: 7=12x+34x23x .Solve: 1=12u+14u23u .Solve: 15(n+3)=14(n+2) .Solve: 12(m4)=14(m7) .Solve: 3r+56+1=4r+33 .Solve: 2s+32+1=3s+24 .Solve: 0.25n+0.05(n+5)=2.95 .Solve: 0.10d+0.05(d5)=2.15 .In the following exercises, determine whether the given values are solutions to the equation. 1. 6y+10=12y (a) y=53 (b) y=12 In the following exercises, determine whether the given values are solutions to the equation. 2. 4x+9=8x (a) x=78 (b) x=94 In the following exercises, determine whether the given values are solutions to the equation. 3. 8u1=6u (a) u=12 (b) u=12 In the following exercises, determine whether the given values are solutions to the equation. 4. 9v2=3v (a) v=13 (b) v=13 In the following exercises, solve each linear equation. 5. 15(y9)=60 In the following exercises, solve each linear equation. 6. 16(3n+4)=32 In the following exercises, solve each linear equation. 7. (w12)=30 In the following exercises, solve each linear equation. 8. (t19)=28 In the following exercises, solve each linear equation. 9. 51+5(4q)=56 In the following exercises, solve each linear equation. 10. 6+6(5k)=15 In the following exercises, solve each linear equation. 11. 3(102x)+54=0 In the following exercises, solve each linear equation. 12. 2(117x)+54=4 In the following exercises, solve each linear equation. 13. 23(9c3)=22 In the following exercises, solve each linear equation. 14. 35(10x5)=27 In the following exercises, solve each linear equation. 15. 15(15c+10)=c+7 In the following exercises, solve each linear equation. 16. 14(20d+12)=d+7 In the following exercises, solve each linear equation. 17. 3(4n1)2=8n+3 In the following exercises, solve each linear equation. 18. 9(2m3)8=4m+7 In the following exercises, solve each linear equation. 19. 12+2(53y)=9(y1)2 In the following exercises, solve each linear equation. 20. 15+4(25y)=7(y4)+4 In the following exercises, solve each linear equation. 21. 5+6(3s5)=3+2(8s1)In the following exercises, solve each linear equation. 22. 12+8(x5)=4+3(5x2)In the following exercises, solve each linear equation. 23. 4(p4)(p+7)=5(p3)In the following exercises, solve each linear equation. 24. 3(a2)(a+6)=4(a1)In the following exercises, solve each linear equation. 25. 4[58(4c3)]=12(113c)8 In the following exercises, solve each linear equation. 26. 5[92(6d1)]=11(410d)139 In the following exercises, solve each linear equation. 27. 3[9+8(4h3)]=2(512h)19 In the following exercises, solve each linear equation. 28. 3[14+2(15k6)]=8(35k)24 In the following exercises, solve each linear equation. 29. 5[2(m+4)+8(m7)]=2[3(5+m)(213m)]In the following exercises, solve each linear equation. 30. 10[5(n+1)+4(n1)]=11[7(5+n)(253n)]In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 31. 23z+19=3(5z9)+8z+46 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 32. 15y+32=2(10y7)5y+46 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 33. 18(5j1)+29=47 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 34. 24(3d4)+100=52 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 35. 22(3m4)=8(2m+9)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 36. 30(2n1)=5(10n+8)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 37. 7v+42=11(3v+8)2(13v1)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 38. 18u51=9(4u+5)6(3u10)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 39. 45(3y2)=9(15y6)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 40. 60(2x1)=15(8x+5)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 41. 9(14d+9)+4d=13(10d+6)+3 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 42. 11(8c+5)8c=2(40c+25)+5 In the following exercises, solve each equation with fraction coefficients. 43. 14x12=34 In the following exercises, solve each equation with fraction coefficients. 44. 34x12=14 In the following exercises, solve each equation with fraction coefficients. 45. 56y23=32 In the following exercises, solve each equation with fraction coefficients. 46. 56y13=76 In the following exercises, solve each equation with fraction coefficients. 47. 12a+38=34 In the following exercises, solve each equation with fraction coefficients. 48. 58b+12=34 In the following exercises, solve each equation with fraction coefficients. 49. 2=13x12x+23x In the following exercises, solve each equation with fraction coefficients. 50. 2=35x13x+25x In the following exercises, solve each equation with fraction coefficients. 51. 13w+54=w14 In the following exercises, solve each equation with fraction coefficients. 52. 12a14=16a+112 In the following exercises, solve each equation with fraction coefficients. 53. 13b+15=25b35 In the following exercises, solve each equation with fraction coefficients. 54. 13x+25=15x25 In the following exercises, solve each equation with fraction coefficients. 55. 14(p7)=13(p+5)In the following exercises, solve each equation with fraction coefficients. 56. 15(q+3)=12(q3)In the following exercises, solve each equation with fraction coefficients. 57. 12(x+4)=34 In the following exercises, solve each equation with fraction coefficients. 58. 13(x+5)=56 In the following exercises, solve each equation with fraction coefficients. 59. 4n+84=n3 In the following exercises, solve each equation with fraction coefficients. 60. 3p+63=p2 In the following exercises, solve each equation with fraction coefficients. 61. 3x+42+1=5x+108 In the following exercises, solve each equation with fraction coefficients. 62. 10y23+3=10y+19 In the following exercises, solve each equation with fraction coefficients. 63. 7u141=4u+85 In the following exercises, solve each equation with fraction coefficients. 64. 3v62+5=11v45 In the following exercises, solve each equation with decimal coefficients. 65. 0.4x+0.6=0.5x1.2 In the following exercises, solve each equation with decimal coefficients. 66. 0.7x+0.4=0.6x+2.4 In the following exercises, solve each equation with decimal coefficients. 67. 0.9x1.25=0.75x+1.75 In the following exercises, solve each equation with decimal coefficients. 68. 1.2x0.91=0.8x+2.29 In the following exercises, solve each equation with decimal coefficients. 69. 0.05n+0.10(n+8)=2.15 In the following exercises, solve each equation with decimal coefficients. 70. 0.05n+0.10(n+7)=3.55 In the following exercises, solve each equation with decimal coefficients. 71. 0.10d+0.25(d+5)=4.05 In the following exercises, solve each equation with decimal coefficients. 72. 0.10d+0.25(d+7)=5.25 Fencing Micah has 74 feet of fencing to make a dog run in his yard. He wants the length to be 2.5 feet more than the width. Find the length, L, by solving the equation 2L+2(L2.5)=74 .Stamps Paula bought $22.82 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was eight less than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s8)=22.82 for s, to find the number of 49-cent stamps Paula bought.Using your own words, list the steps in the general strategy for solving linear equations.Explain why you should simplify both sides of an equation as much as possible before collecting the variable terms to one side and the constant terms to the other side.What is the first step you take when solving the equation 37(y4)=38 ? Why is this your first step?If an equation has several fractions, how does multiplying both sides by the LCD make it easier to solve?If an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?For the equation 0.35x+2.1=3.85 , how do you clear the decimal?Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was three more than twice the number of notebooks. He bought seven textbooks. How many notebooks did he buy?Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is eight more than twice the number of crossword puzzles. He completed 22 Sudoku puzzles. How many crossword puzzles did he do?The sum of four times a number and two is fourteen. Find the number.The sum of three times a number and seven is twenty-five. Find the number.The sum of two numbers is negative twenty-three. One number is seven less than the other. Find the numbers.The sum of two numbers is negative eighteen. One number is forty more than the other. Find the numbers.Find three consecutive integers whose sum is 96 .Find three consecutive integers whose sum is 36 .Find three consecutive even integers whose sum is 102.Find three consecutive even integers whose sum is 24 .According to the National Automobile Dealers Association, the average cost of a car in 2014 was $28,400. This was $1,600 less than six times the cost in 1975. What was the average cost of a car in 1975?US Census data shows that the median price of new home in the U.S. in November 2014 was $280,900. This was $10,700 more than 14 times the price in November 1964. What was the median price of a new home in November 1964?Translate and solve: (a) What number is 45% of 80? (b) 7.5% of what amount is $1.95? (c) 110 is what percent of 88?Translate and solve: (a) What number is 55% of 60? (b) 8.5% of what amount is $3.06? (a) 126 is what percent of 72?One serving of wheat square cereal has 7 grams of fiber, which is 28% of the recommended daily amount. What is the total recommended daily amount of fiber?One serving of rice cereal has 190 mg of sodium, which is 8% of the recommended daily amount. What is the total recommended daily amount of sodium?Mitzi received some gourmet brownies as a gift. The wrapper said each 28% brownie was 480 calories, and had 240 calories of fat. What percent of the total calories in each brownie comes from fat? Round the answer to the nearest whole percent.The mix Ricardo plans to use to make brownies says that each brownie will be 190 calories, and 76 calories are from fat. What percent of the total calories are from fat? Round the answer to the nearest whole percent.Find the percent change. (Round to the nearest tenth of a percent.) In 2011, the IRS increased the deductible mileage cost to 55.5 cents from 51 cents.Find the percent change. (Round to the nearest tenth of a percent.) In 1995, the standard bus fare in Chicago was $1.50. In 2008, the standard bus fare was 2.25.Find (a) the amount of mark-up and (b) the list price: Jim’s music store bought a guitar at original cost $1,200. Jim marked the price up 50%.Find (a) the amount of mark-up and (b) the list price: The Auto Resale Store bought Pablo’s Toyota for $8,500. They marked the price up 35%.Nathaly deposited $12,500 in her bank account where it will earn 4% simple interest. How much interest will Nathaly earn in five years?Susana invested a principal of $36,000 in her bank account that earned simple interest at an interest rate of 6.5%. How much interest did she earn in three years?Jim lent his sister $5,000 to help her buy a house. In three years, she paid him the $5,000, plus $900 interest. What was the rate of simple interest?Loren lent his brother $3,000 to help him buy a car. In four years, his brother paid him back the $3,000 plus $660 in interest. What was the rate of simple interest?Eduardo noticed that his new car loan papers stated that with a 7.5% simple interest rate, he would pay $6,596.25 in interest over five years. How much did he borrow to pay for his car?In five years, Gloria’s bank account earned $2,400 interest at 5% simple interest. How much had she deposited in the account?List five positive thoughts you can say to yourself that will help you approach word problems with a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.List five negative thoughts that you have said to yourself in the past that will hinder your progress on word problems. You may want to write each one on a small piece of paper and rip it up to symbolically destroy the negative thoughts.In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question. 83. There are 16 girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys.In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question. 84. There are 18 Cub Scouts in Troop 645. The number of scouts is three more than five times the number of adult leaders. Find the number of adult leaders.In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question. 85. Huong is organizing paperback and hardback books for her club’s used book sale. The number of paperbacks is 12 less than three times the number of hardbacks. Huong had 162 paperbacks. How many hardback books were there?In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question. 86. Jeff is lining up children’s and adult bicycles at the bike shop where he works. The number of children’s bicycles is nine less than three times the number of adult bicycles. There are 42 adult bicycles. How many children’s bicycles are there?In the following exercises, solve each number word problem. 87. The difference of a number and 12 is three. Find the number.In the following exercises, solve each number word problem. 88. The difference of a number and eight is four. Find the number.In the following exercises, solve each number word problem. 89. The sum of three times a number and eight is 23. Find the number.In the following exercises, solve each number word problem. 90. The sum of twice a number and six is 14. Find the number.In the following exercises, solve each number word problem. 91. The difference of twice a number and seven is 17. Find the number.In the following exercises, solve each number word problem. 92. The difference of four times a number and seven is 21. Find the number.In the following exercises, solve each number word problem. 93. Three times the sum of a number and nine is 12. Find the number.In the following exercises, solve each number word problem. 94. Six times the sum of a number and eight is 30. Find the number.In the following exercises, solve each number word problem. 95. One number is six more than the other. Their sum is 42. Find the numbers.In the following exercises, solve each number word problem. 96. One number is five more than the other. Their sum is 33. Find the numbers.In the following exercises, solve each number word problem. 97. The sum of two numbers is 20. One number is four less than the other. Find the numbers.In the following exercises, solve each number word problem. 98. The sum of two numbers is 27. One number is seven less than the other. Find the numbers.In the following exercises, solve each number word problem. 99. One number is 14 less than another. If their sum is increased by seven, the result is 85. Find the numbers.In the following exercises, solve each number word problem. 100. One number is 11 less than another. If their sum is increased by eight, the result is 71. Find the numbers.In the following exercises, solve each number word problem. 101. The sum of two numbers is 14. One number is two less than three times the other. Find the numbers.In the following exercises, solve each number word problem. 102. The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.In the following exercises, solve each number word problem. 103. The sum of two consecutive integers is 77. Find the integers.In the following exercises, solve each number word problem. 104. The sum of two consecutive integers is 89. Find the integers.In the following exercises, solve each number word problem. 105. The sum of three consecutive integers is 78. Find the integers.In the following exercises, solve each number word problem. 106. The sum of three consecutive integers is 60. Find the integers.In the following exercises, solve each number word problem. 107. Find three consecutive integers whose sum is 36 .In the following exercises, solve each number word problem. 108. Find three consecutive integers whose sum is 3 .In the following exercises, solve each number word problem. 109. Find three consecutive even integers whose sum is 258.In the following exercises, solve each number word problem. 110. Find three consecutive even integers whose sum is 222.In the following exercises, solve each number word problem. 111. Find three consecutive odd integers whose sum is 213 .In the following exercises, solve each number word problem. 112. Find three consecutive odd integers whose sum is 267 .In the following exercises, solve each number word problem. 113. Philip pays $1,620 in rent every month. This amount is $120 more than twice what his brother Paul pays for rent. How much does Paul pay for rent?In the following exercises, solve each number word problem. 114. Marc just bought an SUV for $54,000. This is $7,400 less than twice what his wife paid for her car last year. How much did his wife pay for her car?In the following exercises, solve each number word problem. 115. Laurie has $46,000 invested in stocks and bonds. The amount invested in stocks is $8,000 less than three times the amount invested in bonds. How much does Laurie have invested in bonds?In the following exercises, solve each number word problem. 116. Erica earned a total of $50,450 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than three times the amount she earned from her job at the college. How much did she earn from her job at the college?In the following exercises, translate and solve. 117. (a) What number is 45% of 120? (b) 81 is 75% of what number? (a) What percent of 260 is 78?In the following exercises, translate and solve. 118. (a) What number is 65% of 100? (b) 93 is 75% of what number? (a) What percent of 215 is 86?In the following exercises, translate and solve. 119. (a) 250% of 65 is what number? (b) 8.2% of what amount is $2.87? (a) 30 is what percent of 20?In the following exercises, translate and solve. 120. (a) 150% of 90 is what number? (b) 6.4% of what amount is $2.88? (a) 50 is what percent of 40?In the following exercises, solve. 121. Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. Geneva wants to leave 16% of the total bill as a tip. How much should the tip be?In the following exercises, solve. 122. When Hiro and his co-workers had lunch at a restaurant near their work, the bill was $90.50. They want to leave 18% of the total bill as a tip. How much should the tip be?In the following exercises, solve. 123. One serving of oatmeal has 8 grams of fiber, which is 33% of the recommended daily amount. What is the total recommended daily amount of fiber?In the following exercises, solve. 124. One serving of trail mix has 67 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates?In the following exercises, solve. 125. A bacon cheeseburger at a popular fast food restaurant contains 2070 milligrams (mg) of sodium, which is 86% of the recommended daily amount. What is the total recommended daily amount of sodium?In the following exercises, solve. 126. A grilled chicken salad at a popular fast food restaurant contains 650 milligrams (mg) of sodium, which is 27% of the recommended daily amount. What is the total recommended daily amount of sodium?In the following exercises, solve. 127. The nutrition fact sheet at a fast food restaurant says the fish sandwich has 380 calories, and 171 calories are from fat. What percent of the total calories is from fat?In the following exercises, solve. 128. The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 190 calories, and 114 calories are from fat. What percent of the total calories is from fat?In the following exercises, solve. 129. Emma gets paid $3,000 per month. She pays $750 a month for rent. What percent of her monthly pay goes to rent?In the following exercises, solve. 130. Dimple gets paid $3,200 per month. She pays $960 a month for rent. What percent of her monthly pay goes to rent?In the following exercises, solve. 131. Tamanika received a raise in her hourly pay, from $15.50 to $17.36. Find the percent change.In the following exercises, solve. 132. Ayodele received a raise in her hourly pay, from $24.50 to $25.48. Find the percent change.In the following exercises, solve. 133. Annual student fees at the University of California rose from about $4,000 in 2000 to about $12,000 in 2010. Find the percent change.In the following exercises, solve. 134. The price of a share of one stock rose from $12.50 to $50. Find the percent change.In the following exercises, solve. 135. A grocery store reduced the price of a loaf of bread from $2.80 to $2.73. Find the percent change.In the following exercises, solve. 136. The price of a share of one stock fell from $8.75 to $8.54. Find the percent change.In the following exercises, solve. 137. Hernando’s salary was $49,500 last year. This year his salary was cut to $44,055. Find the percent change.In the following exercises, solve. 138. In ten years, the population of Detroit fell from 950,000 to about 712,500. Find the percent change.In the following exercises, find (a) the amount of discount and (b) the sale price. 139. Janelle bought a beach chair on sale at 60% off. The original price was $44.95.In the following exercises, find (a) the amount of discount and (b) the sale price. 140. Errol bought a skateboard helmet on sale at 40% off. The original price was $49.95.In the following exercises, find (a) the amount of discount and (b) the discount rate (Round to the nearest tenth of a percent if needed.) 141. Larry and Donna bought a sofa at the sale price of $1,344. The original price of the sofa was $1,920.In the following exercises, find (a) the amount of discount and (b) the discount rate (Round to the nearest tenth of a percent if needed.) 142. Hiroshi bought a lawnmower at the sale price of $240. The original price of the lawnmower is $300.In the following exercises, find (a) the amount of the mark-up and (b) the list price. 143. Daria bought a bracelet at original cost $16 to sell in her handicraft store. She marked the price up 45%. What was the list price of the bracelet?In the following exercises, find (a) the amount of the mark-up and (b) the list price. 144. Regina bought a handmade quilt at original cost $120 to sell in her quilt store. She marked the price up 55%. What was the list price of the quilt?In the following exercises, find (a) the amount of the mark-up and (b) the list price. 145. Tom paid $0.60 a pound for tomatoes to sell at his produce store. He added a 33% mark-up. What price did he charge his customers for the tomatoes?In the following exercises, find (a) the amount of the mark-up and (b) the list price. 146. Flora paid her supplier $0.74 a stem for roses to sell at her flower shop. She added an 85% mark-up. What price did she charge her customers for the roses?In the following exercises, solve. 147. Casey deposited $1,450 in a bank account that earned simple interest at an interest rate of 4%. How much interest was earned in two years?In the following exercises, solve. 148. Terrence deposited $5,720 in a bank account that earned simple interest at an interest rate of 6%. How much interest was earned in four years?In the following exercises, solve. 149. Robin deposited $31,000 in a bank account that earned simple interest at an interest rate of 5.2%. How much interest was earned in three years?In the following exercises, solve. 150. Carleen deposited $16,400 in a bank account that earned simple interest at an interest rate of 3.9%. How much interest was earned in eight years?In the following exercises, solve. 151. Hilaria borrowed $8,000 from her grandfather to pay for college. Five years later, she paid him back the $8,000, plus $1,200 interest. What was the rate of simple interest?In the following exercises, solve. 152. Kenneth lent his niece $1,200 to buy a computer. Two years later, she paid him back the $1,200, plus $96 interest. What was the rate of simple interest?In the following exercises, solve. 153. Lebron lent his daughter $20,000 to help her buy a condominium. When she sold the condominium four years later, she paid him the $20,000, plus $3,000 interest. What was the rate of simple interest?In the following exercises, solve. 154. Pablo borrowed $50,000 to start a business. Three years later, he repaid the $50,000, plus $9,375 interest. What was the rate of simple interest?In the following exercises, solve. 155. In 10 years, a bank account that paid 5.25% simple interest earned $18,375 interest. What was the principal of the account?In the following exercises, solve. 156. In 25 years, a bond that paid 4.75% simple interest earned $2,375 interest. What was the principal of the bond?In the following exercises, solve. 157. Joshua’s computer loan statement said he would pay $1,244.34 in simple interest for a three-year loan at 12.4%. How much did Joshua borrow to buy the computer?In the following exercises, solve. 158. Margaret’s car loan statement said she would pay $7,683.20 in simple interest for a five-year loan at 9.8%. How much did Margaret borrow to buy the car?Tipping At the campus coffee cart, a medium coffee costs $1.65. MaryAnne brings $2.00 with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave?Tipping Four friends went out to lunch and the bill came to $53.75 They decided to add enough tip to make a total of $64, so that they could easily split the bill evenly among themselves. What percent tip did they leave?What has been your past experience solving word problems? Where do you see yourself moving forward?Without solving the problem “44 is 80% of what number” think about what the solution might be. Should it be a number that is greater than 44 or less than 44? Explain your reasoning.After returning from vacation, Alex said he should have packed 50% fewer shorts and 200% more shirts. Explain what Alex meant.Because of road construction in one city, commuters were advised to plan that their Monday morning commute would take 150% of their usual commuting time. Explain what this means.Use the formula A=12bh to solve for b.Use the formula A=12bh to solve for h.Solve the formula F=95C+32 for C.Solve the formula A=12h(b+B) for b.Solve the formula A=P+Prt for t.Solve the formula A=P+Prt for r.Solve the formula 4x+7y=9 for y.Solve the formula 5x+8y=1 for y.The area of a triangular church window is 90 square meters. The base of the window is 15 meters. What is the window’s height?A triangular tent door has area 15 square feet. The height is five feet. What is the length of the base?The measure of one angle of a right triangle is 50 more than the measure of the smallest angle. Find the measures of all three angles.The measure of one angle of a right triangle is 30 more than the measure of the smallest angle. Find the measures of all three angles.Use the Pythagorean Theorem to find the length of the leg in the figure.Use the Pythagorean Theorem to find the length of the leg in the figure.The length of a rectangle is seven more than twice the width. The perimeter is 110 inches. Find the length and width.The width of a rectangle is eight yards less than twice the length. The perimeter is 86 yards. Find the length and width.One side of a triangle is seven inches more than the first side. The third side is four inches less than three times the first. The perimeter is 28 inches. Find the length of the three sides of the triangle.One side of a triangle is three feet less than the first side. The third side is five feet less than twice the first. The perimeter is 20 feet. Find the length of the three sides of the triangle.The perimeter of a rectangular swimming pool is 200 feet. The length is 40 feet more than the width. Find the length and width.The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width.John puts the base of a 13-foot ladder five feet from the wall of his house as shown in the figure. How far up the wall does the ladder reach?Randy wants to attach a 17-foot string of lights to the top of the 15 foot mast of his sailboat, as shown in the figure. How far from the base of the mast should he attach the end of the light string?In the following exercises, solve the given formula for the specified variable. 165. Solve the formula C=D for d.In the following exercises, solve the given formula for the specified variable. 166. Solve the formula C=D for p.In the following exercises, solve the given formula for the specified variable. 167. Solve the formula V=LWH for L.In the following exercises, solve the given formula for the specified variable. 168. Solve the formula V=LWH for H.In the following exercises, solve the given formula for the specified variable. 169. Solve the formula A=12bh for b.In the following exercises, solve the given formula for the specified variable. 170. Solve the formula A=12bh for h.In the following exercises, solve the given formula for the specified variable. 171. Solve the formula A=12d1d2 for d1 .In the following exercises, solve the given formula for the specified variable. 172. Solve the formula A=12d1d2 for d2 .In the following exercises, solve the given formula for the specified variable. 173. Solve the formula A=12h(b1+b2) for b1 .In the following exercises, solve the given formula for the specified variable. 174. Solve the formula A=12h(b1+b2) for b2 .In the following exercises, solve the given formula for the specified variable. 175. Solve the formula h=54t+12at2 for a.In the following exercises, solve the given formula for the specified variable. 176. Solve the formula h=48t+12at2 for a.In the following exercises, solve the given formula for the specified variable. 177. Solve 180=a+b+c for a.In the following exercises, solve the given formula for the specified variable. 178. Solve 180=a+b+c for c.In the following exercises, solve the given formula for the specified variable. 179. Solve the formula A=12pl+B for p.In the following exercises, solve the given formula for the specified variable. 180. Solve the formula A=12pl+B for l.In the following exercises, solve the given formula for the specified variable. 181. Solve the formula p=2L+2W for L.In the following exercises, solve the given formula for the specified variable. 182. Solve the formula p=2L+2W for W.In the following exercises, solve for the formula for y. 183. Solve the formula 8x+y=15 for y.In the following exercises, solve for the formula for y. 184. Solve the formula 9x+y=13 for y.In the following exercises, solve for the formula for y. 185. Solve the formula 4x+y=6 for y.In the following exercises, solve for the formula for y. 186. Solve the formula 5x+y=1 for y.In the following exercises, solve for the formula for y. 187. Solve the formula xy=4 for y.In the following exercises, solve for the formula for y. 188. Solve the formula xy=3 for y.In the following exercises, solve for the formula for y. 189. Solve the formula 4x+3y=7 for y.In the following exercises, solve for the formula for y. 190. Solve the formula 3x+2y=11 for y.In the following exercises, solve for the formula for y. 191. Solve the formula 2x+3y=12 for y.In the following exercises, solve for the formula for y. 192. Solve the formula 5x+2y=10 for y.In the following exercises, solve for the formula for y. 193. Solve the formula 3x2y=18 for y.In the following exercises, solve for the formula for y. 194. Solve the formula 4x3y=12 for y.In the following exercises, solve using a geometry formula. 195. A triangular flag has area 0.75 square feet and height 1.5 foot. What is its base?In the following exercises, solve using a geometry formula. 196. A triangular window has area 24 square feet and height six feet. What is its base?In the following exercises, solve using a geometry formula. 197. What is the base of a triangle with area 207 square inches and height 18 inches?In the following exercises, solve using a geometry formula. 198. What is the height of a triangle with area 893 square inches and base 38 inches?In the following exercises, solve using a geometry formula. 199. The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.In the following exercises, solve using a geometry formula. 200. The measure of the smallest angle of a right triangle is 20° less than the measure of the next larger angle. Find the measures of all three angles.In the following exercises, solve using a geometry formula. 201. The angles in a triangle are such that one angle is twice the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.In the following exercises, solve using a geometry formula. 202. The angles in a triangle are such that one angle is 20 more than the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse. 203.In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse. 204.In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse. 205.In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse. 206.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth if necessary. 207.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth if necessary. 208.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth if necessary. 209.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth if necessary. 210.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth if necessary. 211.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth if necessary. 212.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth if necessary. 213.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth if necessary. 214.In the following exercises, solve using a geometry formula. 215. The width of a rectangle is seven meters less than the length. The perimeter is 58 meters. Find the length and width.In the following exercises, solve using a geometry formula. 219. The perimeter of a rectangle of 150 feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.In the following exercises, solve using a geometry formula. 217. The width of the rectangle is 0.7 meters less than the length. The perimeter of a rectangle is 52.6 meters. Find the dimensions of the rectangle.

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